Parallel maximal cliques algorithms for interval graphs with applications

Author

Wang, Chi Su ; Chang, Ruay Shiung

Author_Institution

Dept. of Inf. Manage., Nat. Taiwan Inst. of Technol., Taipei, Taiwan

fYear

1994

fDate

14-16 Dec 1994

Firstpage

89

Lastpage

96

Abstract

In this paper, an O(n log n) time algorithm for finding all the maximal cliques of an interval graph is proposed. This algorithm can also be implemented in parallel in O(log n) time using O(n²) processors. The maximal cliques of an interval graph contain important structural information. Many problems on interval graphs can be solved after all the maximal cliques are known. It is shown that cut vertices, bridges, and vertex connectivities can all be determined easily after the maximal cliques are known. Finally, the all-pair shortest path problem for interval graphs is solved based on the relationship between maximal cliques. The all-pair shortest path algorithm can also be parallelized in O(log n) time using O(n²) processors

Keywords

computational complexity; graph theory; parallel algorithms; all-pair shortest path problem; bridges; cut vertices; interval graph; interval graphs; maximal cliques; parallel maximal cliques algorithms; structural information; vertex connectivities; Bridge circuits; Information management; Mathematical model; NP-complete problem; Parallel architectures; Polynomials; Shortest path problem;

fLanguage

English

Publisher

ieee

Conference_Titel

Parallel Architectures, Algorithms and Networks, 1994. (ISPAN), International Symposium on

Conference_Location

Kanazawa

Print_ISBN

0-8186-6507-6

Type

conf

DOI

10.1109/ISPAN.1994.367160

Filename

367160